Simple Machines.
481
and they can all be placed under two divisions — levers and
inclined planes. There is always a point P where the energy
enters, and a point W where it is removed,"* and the Principle
of Work states that
Work put in at P = work taken out at W
neglecting resistances. But as work = force x distance,
where d = distance travelled by P, and D that travelled by W.
This is the underlying principle, and our investigations on
machines are for the purpose of finding the comparison of the
distances or speeds at P and W, for by inversion we shall obtain
the relation of the forces W and P. The first is the ratio of
virtual velocities and the second is mechanical advantage. Then,
generally,
veLP force W
-— — = - - ~~
vel. W force P
.
= Mech. Adv. -=•*
P
Mech. Adv.
The Lever is shewn under various forms in Fig. 436. By
moments :
Pa - WA and Mech. Adv. - ? - | ^ ****** Z>
P • A p. 763.)
The Wheel and Axle, Fig. 437, is reckoned similarly,
and its
a handle
A "" barrel rad.
A train cf gearing in Fig. 438 consists of two pairs of wheels,
a handle, and a barrel. The advantage of the first pair would
be - : of the second pair •—• : and of the wheel and axle —-. So
A Aj A2
the total
Mech. Adv. -=r- = ~ x -A- x »—•
P A Aj A2
* The old letters P and W being retained, are, meant to represent the forces
and also the points of application. Rankine called them effort and resistance
respectively. Note that fractional and other losses are entirely-neglected on
pp. 481-4 and Theoretical mechanical advantage is therefore the result.
(Sup, 954- )